My text book on probability says "sample spaces with an infinite number of elements are quite common. As an example, consider throwing a dart on a square target and viewing the point of impact as the outcome."
Assuming 'point of impact' denotes the point in the square target where the dart hits, does this infiniteness pertain to infinite number of points in a square? Can anyone give any other example of
- Infinite number of elements in sample space, for a single well defined experiment (not like throwing a dice infinite number of times.)
- "When dealing with probabilistic models involving an uncountably infinite sample space, there are certain unusual subsets for which one cannot associate meaningful probabilities." Any example for this case?